IEEE Trans Vis Comput Graph - Surface Meshing with Curvature Convergence.

Tópicos

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{ imag(2830) propos(1344) filter(1198) }
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Resumo

Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to Riemannian metric and independent of embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm.

Resumo Limpo

surfac mesh play fundament role graphic visual mani geometr process task involv solv geometr pdes mesh numer stabil converg rate approxim error larg determin mesh qualiti practic delaunay refin algorithm offer satisfactori solut high qualiti mesh generat theoret proof volum base surfac base delaunay refin algorithm establish conform parameter base one remain wide open work focus curvatur measur converg conform parameter base delaunay refin algorithm given metric surfac propos approach triangul conform uniform domain planar delaunay refin algorithm produc high qualiti mesh give explicit estim hausdorff distanc normal deviat differ curvatur measur surfac mesh contrast convent result base volumetr delaunay refin stronger estim independ mesh structur direct guarante converg curvatur measur meanwhil result gaussian curvatur measur intrins riemannian metric independ embed practic mesh algorithm much easier implement much effici experiment result verifi theoret result demonstr effici mesh algorithm

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